In a bag there are coins of 25p, 10p and 5p in the ratio 1:2:3.If ther...
Answer – D) 75 Explanation : [(25x) + (10x × 2) + (5x × 3)] / 100 = 45 [25x + 20x + 15x] / 100 = 45 60 x = 4500 X = 4500/60 = 75
In a bag there are coins of 25p, 10p and 5p in the ratio 1:2:3.If ther...
Given Information:
- Coins in the bag: 25p, 10p, and 5p
- Ratio of coins: 1:2:3
- Total amount in the bag: Rs. 45
To find the number of 25p coins, we need to follow these steps:
Step 1: Calculating the total number of coins
- Let's assume the ratio of 25p, 10p, and 5p coins to be x, 2x, and 3x respectively.
- Since the total amount in the bag is Rs. 45, we can write the equation:
25p(x) + 10p(2x) + 5p(3x) = 45
Simplifying the equation:
25x + 20x + 15x = 45
60x = 45
x = 45/60
x = 3/4
Step 2: Calculating the number of 25p coins
- Since the ratio of 25p coins to other coins is x:2x:3x, the number of 25p coins would be (x/6) * Total number of coins.
- Substituting the value of x, we get:
Number of 25p coins = (3/4)/6 * Total number of coins
Number of 25p coins = 3/24 * Total number of coins
Number of 25p coins = Total number of coins/8
Step 3: Calculating the total number of coins
- Since the total number of coins is the sum of the individual coins in the ratio, we can write:
Total number of coins = x + 2x + 3x
Total number of coins = 6x
Substituting the value of x, we get:
Total number of coins = 6 * (3/4)
Total number of coins = 18/4
Total number of coins = 9/2
Step 4: Calculating the number of 25p coins (continued)
- Substituting the value of the total number of coins, we get:
Number of 25p coins = (9/2)/8
Number of 25p coins = 9/2 * 1/8
Number of 25p coins = 9/16
Since the number of coins cannot be in fractional form, we need to find the closest whole number.
Step 5: Rounding the number of 25p coins
- Rounding 9/16 to the nearest whole number, we get:
Number of 25p coins ≈ 1 (as 9/16 is closer to 1 than 0)
Therefore, the number of 25p coins is 1.
Conclusion:
The correct answer is option D) 75.